Optimal control and infectiology: Application to an HIV/AIDS model

Applied Mathematics and Computation

Volumn 177, Issue 2, 2006, Pages 807-818

  Karrakchou, J ^a   Rachik, M ^b   Gourari, S ^a  

^a MOHAMMED V UNIVERSITY   (Morocco)

^b FACULTÉ DES SCIENCES BEN M SIK   (Morocco)

Author keywords

Chemotherapy; HIV AIDS; Infectiology; Optimal control

Indexed keywords

BIOLOGICAL ORGANS; CHEMOTHERAPY; DISEASES; IMMUNOLOGY; OPTIMAL CONTROL SYSTEMS; VIRUSES;

CHEMOTHERAPY TREATMENT; HIV INFECTIONS; HIV/AIDS; INFECTIOLOGY;

EPIDEMIOLOGY;

EID: 33744999665     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.11.092     Document Type: Article

References (19)

1. Anderson R.M. The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS. JAIDS 1 (1988) 241-256
2. In: Anderson R.M., and May R.M. (Eds). Infectious Diseases of Humans: Dynamics and Control (1991), Oxford University Press, Oxford, UK
3. Anderson R.M., Medley G.P., May R.M., and Johnson A.M. A preliminary study of the transmission dynamics of the human immunodeficiency virus, the causative agent of AIDS. IMA J. Math. Appl. Med. Biol. 3 (1986) 229-263
4. +T lymphocytes in HIV-1 disease progression. JAIDS J. Acquired Immune Deficiency Syndromes 30 (2002) 41-58
5. Becker N. The use of epidemic models. Biometrics 35 (1978) 295-305
6. McCluskey C. A model of HIV/AIDS with staged progression and amelioration. Math. Biosci. 181 (2003) 1-16
7. Craig I.K., Xia X., and Venter J.W. Introducing HIV/AIDS education into the electrical engineering curriculum at the University of Pretoria. IEEE Trans. Education 47 Feb. (2004) 65-73
8. Faurre P. Analyse Numérique-Notes d'Optimisation. Ellipses (1988)
9. Fister K.R., Lenhart S., and Nally M.C. Optimizing chemotherapy in an HIV model. Electron. J. Different. Eqns. 32 (1998) 1-12
10. Fleming W.H., and Rishel R.W. Deterministic and Stochastic Optimal Control (1975), Springer, New York
11. A.B. Gumel, P.N. Shivakumar, B.M. Sahai, A mathematical model for the dynamics of HIV-1 during the typical course of infection, in: Third World Congress of Nonlinear Analysts, vol. 47, 2001, pp. 2073-2083.
12. Hethcote H.W. A thousand and one epidemic models. In: Levin S.A. (Ed). Fronters in Theoretical Biology. Lecture Notes in Biomath. vol. 100 (1994), Springer-Verlag, Berlin 504-515
13. Hyman J.M., and Stanley E.A. Using mathematical models to understand the AIDS epidemic. Math. Biosci. 90 (1988) 415-473
14. Joshi H.R. Optimal control of an HIV immunology model. Opt. Control Appl. Meth. 23 (2002) 199-213
15. H.R. Joshi, Optimal Control Problems in PDE and ODE Systems, Thesis of Doctorate, University of Tennessee, USA, May 2002.
16. Kirschner D., Lenhart S., and Serbin S. Optimal Control of the Chemotherapy of HIV. J. Math. Biol. 35 (1997) 775-792
17. J.J. Kutch, P. Gurfil, Optimal control of HIV infection with a continuously-mutating viral population, in: Proceeding of the American Control Conference Anchorage, AK May 8-10, 2002.
18. Lukes D.L. Differential Equations: Classical to Controlled, Mathematics in Science and Engineering (1982), Academic Press, New York
19. Tully D. Optimizing Chemotherapy in an HIV Model (1999), College of the Redwoods, Springer